Elimination+Method+B-1

**Elimination Method**
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The Elimination Method is a way to solve for the point of intersection of two or more equations. The Elimination Method may not always be fast but it is efficient. The process requires the successful execution of the following steps:
 * 1) Eliminating a variable in a system of equations by either subtracting or adding them together in combination with multiplication and division.
 * 2) Once you've eliminated one variable, you can solve for the other variable.
 * 3) Once you've solved for that variable, you can substitute it's value into one of the original equations to solve for the other variable.

__**Example #1**__
Find the solution to these systems of linear equations using the ELIMINATION METHOD. x + 2y = 16 -x +y = 2 __-x +y = 2__ 3y = 18 || eliminate the variable "x" by adding these two equations to each other. || 3 || Solve for 'y' by dividing both sides by 3. || -x + 6 -6 = 2 - 6 __-x = -4__ -1 Checking your solution ** 4 + 12 = 16 ||  ||=  -4 +6 = 2   ||
 * ** Step 1 ** ||= x + 2y = 16
 * ** Step 2 ** ||= __3y = 18__
 * ** Step 3 ** ||= ** y = 6 ** || Plug this value into one of the original equations and solve for x ||
 * ||= -x + y = 2 || Let' s use the second equation ||
 * ||= -x + 6 = 2
 * x = 4 ** || So the point** (4, 6) ** is the only point that satisfies both equations. ||
 * = x + 2y = 16 ||  ||= -x +y = 2 ||
 * = 4 + 2(6) = 16
 * 16 = 16 **
 * 2 = 2 **

__** Example #2 **__
Find the solution to these systems of linear equations using the ELIMINATION METHOD. 5//x//-4//y// = 7 2//y//+6//x// = 22 2(2//y//+6x)=2(22) || First, multiply both sides of the second equation by 2 in order to get 4//y// so that the -4//y// from the first equation cancels out when added to the 4//y// from the second equation. || __4//y//+12//x//=44__ 17//x//+0//y//=51 || Add the two equations together in order to eliminate the variable "y" || 17 || To solve for //x,// you divide both sides of the equation by 17: || 5(3)-4//y//=7 15 -4//y-15//=7//-15// __-4y = -8__ -4
 * ** Step 1 ** ||= 5//x//- 4//y// = 7
 * ||= 5//x//- 4//y// = 7
 * ** Step 2 ** ||= __17x = 51__
 * ** Step 3 ** ||= ** x = 3 ** || Now you have to solve for //y//, and to do this, the first step would be to substitute 3 for //x// in either of the original equations. ||
 * ||= 5//x//-4//y// =7
 * y= 2 ** || Using the first equation, solve for y. ||
 * ||= ** (3, 2) ** || Now use the numbers that were found for the //x// and //y// variables and the solution of the system is ** (3, 2) **. ||

**Checking your Solution** 15- 8 = 7 ** 7=7 ** ||= 2(2) + 6(3) = 22 4+18=22 ** 22 = 22 **  ||
 * = 5//x//-4//y// =7 ||= 2//y//+6//x// = 22 ||
 * = 5(3)-4//(2)// =7

Further Discussion

 * How else could you determine the intersection points for a system of equations?
 * When will there be more then one point of intersection for a pair of equations?